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Understanding the physics of large cosmological surveys down to small (nonlinear) scales will significantly improve our knowledge of the Universe. Large N-body simulations have been built to obtain predictions in the non-linear regime.…
In this review we discuss the works in the area of quantum simulation and many-body physics with light, from the early proposals on equilibrium models to the more recent works in driven dissipative platforms. We start by describing the…
Only through resonances can non-axisymmetric features such as spiral arms and bars exert torques over large scales and change the overall structure of a near-equilibrium galaxy. We describe the resonant interaction mechanism in detail and…
We describe recent progress in the statistical mechanical description of many-body systems via machine learning combined with concepts from density functional theory and many-body simulations. We argue that the neural functional theory by…
In this paper I focus on three topics related to the dynamical evolution of small galaxy groups, for which the input of N-body simulations has been decisive. These are the merging rates in compact groups, the properties of remnants of…
It is crucial to understand and model a behavior of galaxy biasing for future ambitious galaxy redshift surveys. Using 40 large cosmological N-body simulations for a standard LambdaCDM cosmology, we study the cross-correlation coefficient…
A collisional $N$-body simulation using NBODY5 on a single CRAY YMP processor is followed well into the post-collapse regime. This is presently one of the largest particle numbers of all such models published, but some data for an even…
As a complement to experimental and theoretical approaches, numerical modeling has become an important component to study asteroid collisions and impact processes. In the last decade, there have been significant advances in both…
We show and interpret three examples of nontrivial results obtained in numerical simulations of many-body systems: exponential convergence of low-lying energy eigenvalues in the process of progressive truncation of huge shell-model…
We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low…
Several physical systems in condensed matter have been modeled approximating their constituent particles as hard objects. The hard spheres model has been indeed one of the cornerstones of the computational and theoretical description in…
A criterion for the choice of optimal softening length $\epsilon$ and time-step $dt$ for $N$-body simulations of a collisionless stellar system is analyzed. Plummer and Hernquist spheres are used as models to follow how changes in various…
A recent description of an exact map for the equilibrium structure and thermodynamics of a quantum system onto a corresponding classical system is summarized. Approximate implementations are constructed by pinning exact limits (ideal gas,…
In the mean field limit, isolated gravitational systems often evolve towards a steady state through a violent relaxation phase. One question is to understand the nature of this relaxation phase, in particular the role of radial…
The theory and application of numerical methods for unstructured meshes have been improved significantly in recent years. Because the grids can be place arbitrarily in space, unstructured meshes can provide much higher spatial resolution…
The mildly non-linear regime of cosmic structure formation holds much of the information that upcoming large-scale structure surveys aim to exploit, making fast and accurate predictions on these scales essential. We present the $N$-body…
Modeling many-body quantum systems with strong interactions is one of the core challenges of modern physics. A range of methods has been developed to approach this task, each with its own idiosyncrasies, approximations, and realm of…
An algorithm is derived for computer simulation of geodesics on the constant potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic…
We describe a novel N-body code designed for simulations of the central regions of galaxies containing massive black holes. The code incorporates Mikkola's 'algorithmic' chain regularization scheme including post-Newtonian terms up to PN2.5…
This article presents several challenges to nuclear many-body theory and our understanding of the stability of nuclear matte r. In order to achieve this, we present five different cases, starting with an idealized toy model. These cases…